Question 10
Factorise each of the following:
$(i) 27 y^{3} + 125 z^{3}$
$(i i) 64 m^{3} - 343 n^{3}$

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Solution

$(i) 27 y^{3} + 125 z^{3} = (3 y)^{3} + (5 z)^{3} [U s i n g i d e n t i t y a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})] = (3 y + 5 z) [(3 y)^{2} - (3 y) (5 z) + (5 z)^{2}] = (3 y + 5 z) (9 y^{2} - 15 y z + 25 z^{2})$

$(i i) 64 m^{3} - 343 n^{3} = (4 m)^{3} - (7 n)^{3} [U s i n g i d e n t i t y a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})] = (4 m - 7 n) [(4 m)^{2} + (4 m) (7 n) + (7 n)^{2}] = (4 m - 7 n) (16 m^{2} + 28 m n + 49 n^{2})$

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Similar questions

Factorise each of the following:

(i)

(ii)

[Hint: See question 9.]

Factorise each of the following:
(i) $27 y^{3} + 125 z^{3}$
(ii) $64 m^{3} - 343 n^{3}$

(i) 27 y^{3} + 125 z^{3}

(i i) 64 m^{3} - 343 n^{3}

64 m^{3} - 343 n^{3}

64 m^{3} - 343 n^{3}

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